Has my birth control failed?

Starting your next pack right away is not going to do anything except possibly stop you from having you period at all. It will not stop you from being pregnant if you are and it will not stop you from becoming pregnant. If you are not on an antibiotic and you have taken the pill EVERYDAY as you say you have then you should be absolutely fine. When you first start BC it can take a few months to have your periods become regulated. Just calm down and wait a few more days and I'm sure it will come. Also, if becoming pregnant is absolutely the worst thing you could ever imagine happening to you then you need to think about using a backup method such as condoms just to double protect yourself.